Question
Three resistance $$P,Q,R$$ each of $$2\,\Omega $$ and an unknown resistance $$S$$ form the four arms of a Wheatstone bridge circuit. When a resistance of $$6\,\Omega $$ is connected in parallel to $$S$$ the bridge gets balanced. What is the value of $$S$$?
A.
$$2\,\Omega $$
B.
$$3\,\Omega $$
C.
$$6\,\Omega $$
D.
$$1\,\Omega $$
Answer :
$$3\,\Omega $$
Solution :
Balancing condition of Wheatstone bridge is used to calculate the value of unknown resistance.
The situation can be depicted as shown in figure.
As resistances $$S$$ and $$6\,\Omega $$ are in parallel their effective resistance is
$$\frac{{6S}}{{6 + S}}\Omega $$
As the bridge is balanced, hence it is balanced Wheatstone bridge.
For balancing condition,
$$\eqalign{ & \frac{P}{Q} = \frac{R}{{\left( {\frac{{6S}}{{6 + S}}} \right)}} \cr & {\text{or}}\,\,\frac{2}{2} = \frac{{2\left( {6 + S} \right)}}{{6S}} \cr & {\text{or}}\,\,3S = 6 + S \cr & {\text{or}}\,\,S = 3\,\Omega \cr} $$
Balancing condition of Wheatstone bridge is used to calculate the value of unknown resistance.
The situation can be depicted as shown in figure.
As resistances $$S$$ and $$6\,\Omega $$ are in parallel their effective resistance is
$$\frac{{6S}}{{6 + S}}\Omega $$
As the bridge is balanced, hence it is balanced Wheatstone bridge.
For balancing condition,
$$\eqalign{ & \frac{P}{Q} = \frac{R}{{\left( {\frac{{6S}}{{6 + S}}} \right)}} \cr & {\text{or}}\,\,\frac{2}{2} = \frac{{2\left( {6 + S} \right)}}{{6S}} \cr & {\text{or}}\,\,3S = 6 + S \cr & {\text{or}}\,\,S = 3\,\Omega \cr} $$
